Unreliable Symbols Research Articles

High-Performance Soft Decision Decoding for Compound Channel Using RS-SPC Concatenated Codes

A novel single parity check-assisted ordered statistic decoding (SPC-OSD) algorithm for the compound channel is proposed for Reed-Solomon (RS) codes. The algorithm can effectively use the channel soft information to accurately determine the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N - K</i> unreliable symbol positions to be erased by using single parity checking and threshold comparison. Besides that, the second-burst error symbol is also proposed as a supplement to unreliable symbols. Based on these predetermined errors, the algorithm can be dynamically adjusted according to the channel environment to achieve the best decoding performance. Compared with burst-error correcting algorithm-based ordered-statistics decoding (BC-OSD) and burst error correcting hard-decision decoding-based low-complexity chase algorithm (BCHDD-LCC), simulation results show that the proposed algorithm can give a coding gain reaching up to 2.0dB and 2.1dB respectively, when symbol error rate (SER) is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> .

Low-Complexity Chase Decoding of Reed-Solomon Codes Using Module

The interpolation based algebraic soft decoding yields a high decoding performance for Reed-Solomon (RS) codes with a polynomial-time complexity. Its computationally expensive interpolation can be facilitated using the module structure. The desired Grobner basis can be achieved by reducing the basis of a module. This paper proposes the low-complexity Chase (LCC) decoding algorithm using this module basis reduction (BR) interpolation technique, namely the LCC-BR algorithm. By identifying $\eta $ unreliable symbols, $2^\eta $ decoding test-vectors will be formulated. The LCC-BR algorithm first constructs a common basis which will be shared by the decoding of all test-vectors. This eliminates the redundant computation in decoding each test-vector, resulting in a lower decoding complexity and latency. This paper further proposes the progressive LCC-BR algorithm that decodes the test-vectors sequentially and terminates once the maximum-likelihood decision decoding outcome is reached. Exploiting the difference between the adjacent test-vectors, this progressive decoding is realized without any additional memory cost. Complexity analysis shows that the LCC-BR algorithm yields a lower complexity and latency, especially for high rate codes, which will be validated by the numerical results.

An Efficient Post-Processor for Lowering the Error Floor of LDPC Codes

Error floor is one major reason for limited use of low-density parity-check (LDPC) codes in applications requiring very low bit error rate. In this brief, an efficient erasure searching post-processor (ESPP) is proposed to lower the error floor of LDPC codes. Here, when a decoding failure is detected, the most unreliable symbols in the decoder output vector are erased, then their values are re-calculated by solving a system of linear equations with a sparse coefficient matrix. Compared to the state-of-the-art post processors, the ESPP has much lower computation complexity. Simulation results show that the proposed method significantly improves the decoding performance of LDPC codes in the error-floor region. Additionally, a well-optimized hardware architecture is developed for the proposed post-processor. Algorithmic transformation and architecture optimization are well explored to reduce the hardware complexity and latency. Synthesis results demonstrate the effectiveness of the proposed architecture.

Interpolation-Based Low-Complexity Chase Decoding Algorithms for Hermitian Codes

Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding algorithms for one of the most popular AG codes-Hermitian codes. By choosing $\eta $ unreliable symbols and realizing them with the two most likely decisions, $2^\eta $ decoding test-vectors can be formulated. The first LCC algorithm performs interpolation for the common elements of the test-vectors, producing an intermediate outcome that will be shared by the uncommon element interpolation. It eliminates the redundant computation for decoding each test-vector, resulting in a low-complexity. With an interpolation multiplicity of one, the decoding is further facilitated by removing the requirement of pre-calculating the Hermitian curve’s corresponding coefficients. The second LCC algorithm is an adaptive variant of the first algorithm, where the number of test-vectors is determined by the reliability of received information. When the channel condition improves, it can reduce the complexity without compromising the decoding performance. Simulation results show that the both LCC algorithms outperform a number of existing algebraic decoding algorithms for Hermitian codes. Finally, our complexity analysis will reveal the proposals’ low-complexity feature.

Iterative detection for frequency-asynchronous distributed Alamouti-coded (FADAC) OFDM

We propose a near intercarrier interference (ICI)-free and very low complexity iterative detector for frequency-asynchronous distributed Alamouti-coded (FADAC) orthogonal frequency division multiplexing (OFDM). In the previous cancelation schemes, the entire subcarrier signals from one transmit (TX) antenna are estimated and canceled in the received signal from the other TX antenna and vice versa. However, the reliability of the estimated symbols are revealed to significantly vary across the subcarriers and thus, the poorly estimated symbols lead to the incorrect cancelation. Motivated from this, we first propose a scheme which does not cancel the interfering subcarrier(s) at the half band edges which undergo very high interference in FADAC-OFDM. For further improvement, we propose a so-called selective scheme which instantly measures the reliability of the detected symbols at each iteration and then exclude the unreliable symbols in the estimated interference generation.Moreover, the proposed scheme has a drastically reduced complexity by converting the cancelation process from the subcarrier domain to the time domain. In accordance with the analysis on the considered reliability measures, the numerical results show that the proposed scheme achieves the near ICI-free level only within three or four iterations for wide ranges of SNR, frequency offset, and delay spread.

Low-Complexity Group Alternate Iterative List Detection for MIMO Systems

In this paper, we propose a low-complexity group alternate iterative list (GAIL) detection algorithm for MIMO systems. By utilizing the recursive interference suppression and successive interference cancellation techniques, the symbol vector can be partitioned into many subgroups. Subsequently, symbols in each subgroup are detected in terms of the K-best detector. The inter-group interference is effectively mitigated in the GAIL algorithm by creating a candidate list and iteratively correcting the unreliable symbols for the detection result. We provide the performance-complexity tradeoff based on different feasible parameter settings. The numerical results demonstrate that the GAIL algorithm can achieve close-to-optimal performance while maintaining low computational complexity. In addition, the running speed of the GAIL algorithm can be dramatically increased using parallel processing in real-time communication systems.

A reduced-complexity near-ML detection for broadband single-carrier transmission

In our recently proposed reduced-complexity near-maximum likelihood block signal detection employing QR decomposition and Malgorithm (QRM-MLBD) for broadband single-carrier (SC) block transmission, unreliable symbol candidates are removed from the symbol tree based on the hard-decision minimum mean square error based frequencydomain equalization (MMSE-FDE). In this paper, to further remove the unreliable symbol candidates and consequently reduce the computational complexity, we introduce a soft-decision MMSE-FDE based selection of reliable symbol candidates into reduced-complexity QRM-MLBD. It is shown that the soft-decision MMSE-FDE based selection significantly reduces the computational complexity while achieving a bit error rate (BER) performance similar to the original QRM-MLBD.

Novel Techniques to Minimize the Error Propagation of Decision Feedback Equalizer in 8VSB DTV System

In this paper, novel and yet simple techniques are presented to minimize the error propagation caused by the large precursors and postcursors of the decision feedback equalizer (DFE) in 8VSB DTV system. A technique that selects a reference tap (symbol timing of DFE) from an estimated channel impulse response (CIR) is presented to minimize the effect of the large precursors. Another technique that selects the reference tap position, i.e., decision delay in a feedforward filter (FFF), from the estimated CIR and the amplitude of the selected reference tap is proposed to minimize the effect of large postcursors. The combined structure of a feedback filter (FBF) and Viterbi decoder for use in 8VSB DTV system is also proposed to replace the past unreliable decision symbols in FBF as well as to reduce the decision error probability. Simulation results show that our proposed DFE can prevent effectively the error propagation, in particular, by changing the reference tap and its position in FFF according to the channel condition. It is also shown that an echo removing capability of the proposed DFE, where 400 and 620taps are used for the FFF and FBF, respectively, is greater than that of conventional DFEs by about -20 mus in the single pre-echo of -10 dB channel and by about 10 mus in the single post-echo of -1 dB channel

Erased-Chase decoding for RS-coded MPSK signaling over a Rayleigh fading channel

In this paper, a novel dual-metric, the maximum and minimum Squared Euclidean Distance Increment (SEDI) brought by changing the hard decision symbol, is introduced to measure the reliability of the received M-ary Phase Shift Keying (MPSK) symbols over a Rayleigh fading channel. Based on the dual-metric, a Chase-type soft decoding algorithm, which is called erased-Chase algorithm, is developed for Reed-Solomon (RS) coded MPSK schemes. The proposed algorithm treats the unreliable symbols with small maximum SEDI as erasures, and tests the non-erased unreliable symbols with small minimum SEDI as the Chase-2 algorithm does. By introducing optimality test into the decoding procedure, much more reduction in the decoding complexity can be achieved. Simulation results of the RS(63, 42, 22)-coded 8-PSK scheme over a Rayleigh fading channel show that the proposed algorithm provides a very efficient tradeoff between the decoding complexity and the error performance. Finally, an adaptive scheme for the number of erasures is introduced into the decoding algorithm.

Algebraic Soft-Decision Decoding of Reed-Solomon Codes with Erasures on Gaussian Channels

The search for increasing the error performance of algebraic soft-decision decoding of high rate Reed-Solomon (RS) codes motivates the development of this work in an attempt to determine the ultimate error-correcting capabilities of algebraic soft-decision decoding of RS codes in Gaussian channels with erasures. It is shown through simulation that a significant performance improvement can be obtained when the unreliable bits received from channel output are declared as erased bits. An alternative method to construct the reliability matrix is developed through the mapping of the a posteriori channel probabilities in order to assign equal multiplicity for symbols with the same erased bits patterns. Conversely, it is also shown through simulation that trying to declare the unreliable symbols received from the channel as erasures does not lead to any performance gain and in some cases it would affect the decoder performance.

Staggered interleaving and iterative errors-and-erasures decoding for frequency-hop packet radio

Information about the reliabilities; of the received symbols is very beneficial in frequency-hop communication systems. This information, known as side information, can be used to erase unreliable symbols at the input to an errors-and-erasures decoder. For slow-frequency-hop systems it is common that special redundant symbols, referred to as side-information symbols, are included in each dwell interval, and the demodulation of these symbols provides the side information. The corresponding decrease in the number of message symbols that can be sent in each dwell interval makes it desirable to develop alternative methods that do not require side-information symbols. In this paper, one such alternative is proposed, and its performance is evaluated for channels with partial-band interference. It is shown that staggered interleaving of Reed-Solomon code words and iterative errors-and-erasures decoding facilitates the erasure of unreliable symbols without the need for side-information symbols. The performance of this method is compared with the performance of systems that employ standard block interleaving and errors-only decoding or errors-and-erasures decoding with side information obtained from test symbols.

Bayesian methods for erasure insertion in frequency-hop communication systems with partial-band interference

The erasure of unreliable symbols improves the performance of most types of error-control coding if a good method is used to decide which symbols should be erased. Bayesian decision theory is employed to obtain such a method for use in frequency-hop communications with Reed-Solomon coding and errors-and-erasures decoding. The performance of frequency-hop communications with Bayesian erasure insertion is analyzed for channels with both partial-band and wideband Gaussian noise. The Bayesian technique is compared with Viterbi's ratio-threshold test, and these are compared to receivers that do not erase and use errors-only decoding. Comparisons are also made with receivers that erase all the symbols that are affected by the partial-band interference. When interference is strong, large coding gains result from the Bayesian method, and error probabilities are reduced by several orders of magnitude.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>